A Morse-Bott unification of the Grassmannians of a symplectic vector space
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917240687820800 |
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| author | Kim, Hyunmoon |
| author_facet | Kim, Hyunmoon |
| contents | We construct a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. We show that its critical loci consist of linear subspaces that split into isotropic and complex parts and that its stable manifolds coincide with the orbits of the linear symplectomorphism group. These orbits generalize the Lagrangian, symplectic, isotropic, and coisotropic Grassmannians to include the Grassmannians of linear subspaces that are neither isotropic, coisotropic, nor symplectic. The negative gradient flow deformation retracts these spaces onto compact homogeneous spaces for the unitary group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16441 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Morse-Bott unification of the Grassmannians of a symplectic vector space Kim, Hyunmoon Symplectic Geometry Differential Geometry 53D05, 57R70, 53D12 We construct a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. We show that its critical loci consist of linear subspaces that split into isotropic and complex parts and that its stable manifolds coincide with the orbits of the linear symplectomorphism group. These orbits generalize the Lagrangian, symplectic, isotropic, and coisotropic Grassmannians to include the Grassmannians of linear subspaces that are neither isotropic, coisotropic, nor symplectic. The negative gradient flow deformation retracts these spaces onto compact homogeneous spaces for the unitary group. |
| title | A Morse-Bott unification of the Grassmannians of a symplectic vector space |
| topic | Symplectic Geometry Differential Geometry 53D05, 57R70, 53D12 |
| url | https://arxiv.org/abs/2601.16441 |